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Implicit, manifold-preserving numerical representations and solvers for multiscale kinetic simulations of plasmas

Presentation Conclusions: We have derived manifold-preserving algorithms for kinetic plasma simulation; Collisionless (PIC): we have solved the 40-year-old algorithmic challenge of developing accurate implicit PIC algorithms; Collisional (VFP): we have demonstrated a truly multiscale algorithm that has enabled routine simulation of ICF spherical capsule implosions with a few hundred cores for a couple of days.; In both cases: Strict conservation properties have been shown to be critical for long-term accuracy.; Significant algorithmic acceleration has been achieved by using nested asymptotic models.; We have seen similar benefits in other applications

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Unsupervised discovery of nonlinear plasma physics using differentiable kinetic simulations

Plasma supports collective modes and particle–wave interactions that lead to complex behaviour in, for example, inertial fusion energy applications. While plasma can sometimes be modelled as a charged fluid, a kinetic description is often crucial for studying nonlinear effects in the higher-dimensional momentum–position phase space that describes the full complexity of the plasma dynamics. We create a differentiable solver for the three-dimensional partial-differential equation describing the plasma kinetics and introduce a domain-specific objective function. Using this framework, we perform gradient-based optimization of neural networks that provide forcing function parameters to the differentiable solver given a set of initial conditions. We apply this to an inertial-fusion-relevant configuration and find that the optimization process exploits a novel physical effect.

plasma nonlinear phenomena↗

Simulations of divertor plasmas with inverse sheaths

The effect of strong electron emission from material surfaces has been proposed to form an “inverse sheath”: a region with a positive potential relative to the near-wall plasma which prevents the flow of ions to the wall [M. D. Campanell, “Negative plasma potential relative to electronemitting surfaces,” Phys. Rev. E. 88, 033103 (2013); M. D. Campanell and M. V. Umansky, “Strongly emitting surfaces unable to float below plasma potential,” Phys. Rev. Lett. 116, 1–5 (2016); M. D. Campanell and G. R. Johnson, “Thermionic cooling of the target plasma to a sub-ev temperature,” Phys. Rev. Lett. 122, 1–5 (2019)]. We assess the viability of this regime in a tokamak device using the 2D edge plasma transport code UEDGE [T. Rognlien et al ., “A fully implicit, time dependent 2-D fluid code for modeling tokamak edge plasmas,” J. Nucl. Mater. 196–198, 347–351 (1992)]. Since the UEDGE code does not consider the sheath region directly, we apply boundary conditions at the divertor targets which emulate the physics of both “standard” and “inverse” sheath regimes [R. Masline et al ., “Influence of the inverse sheath on divertor plasma performance in tokamak edge plasma simulations,” Contrib. Plasma Phys. 60, e201900097 (2020)]. Using these boundary conditions, we perform scoping studies to assess plasma parameters near the target by varying the density at the core-edge interface. We observe a smooth transition in the resultant profiles of plasma parameters for the standard sheath, and a bifurcation across the simulation set for plasmas with an inverse sheath. The cause of this bifurcation is assessed by performing the parameter scan both with and without impurity radiation; we observe that the bifurcation persists in both cases, indicating that this bifurcation is caused by plasma recombination.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

SOLEDGE3X full vessel plasma boundary simulations of ITER non-active phase plasmas

The onset of detachment in the ITER machine is analyzed in this work through the help of 2D-axisymmetric boundary plasma simulations with the SOLEDGE3X-EIRENE code, which features a numerical domain for the plasma solver extending up to the first wall. The plasma boundary is computed in scenarios from the first non-active phase of ITER, in pure H and at 20 MW. This set of simulations is used in two aspects: first, to study the plasma detachment in the divertor, and second, the plasma conditions, fluxes, and beryllium erosion at the first wall. Here, the code results are also compared to those obtained with the well-established SOLPS-ITER code, which includes a plasma numerical domain only covering the main SOL. Results show an increase in the SOL width λ q with increasing density, and a detailed analysis is carried out, for the first time, on each of the different plasma-neutral interactions in the code’s physics model in EIRENE. The gross beryllium erosion rates of first wall panels are estimated from 2D simulations, with the aim of assessing their sensitivity to two parameters: the divertor density regime, and the presence of density shoulders in the far-SOL formed by enhanced perpendicular transport at this location. The erosion contributions from neutrals and ions are considered in each case, and the charge-exchange atoms fluxes and energy distributions are provided, highlighting the two atom populations (cold and charge-exchange).

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

High-order two-fluid plasma solver for direct numerical simulations of plasma flows with full transport phenomena

The two-fluid plasma equations for a single ion species, with full transport terms, including temperature and magnetic field dependent ion and electron viscous stresses and heat fluxes, frictional drag force, and ohmic heating terms, have been implemented in the CFDNS code and solved by using sixth-order non-dissipative compact finite differences for plasma flows in several different regimes. In order to be able to fully resolve all the dynamically relevant time and length scales, while maintaining computational feasibility, the assumptions of infinite speed of light and negligible electron inertia have been made. Non-dimensional analysis of the two-fluid plasma equations shows that, by varying the characteristic/background number density, length scale, temperature, and magnetic strength, the corresponding Hall, resistive, and ideal magnetohydrodynamic equations can be recovered as limiting cases. The accuracy and robustness of this two-fluid plasma solver in handling plasma flows in different regimes have been validated against four canonical problems: Alfven and whistler dispersion relations, electromagnetic plasma shock, and magnetic reconnection. For all test cases, by using physical dissipation and diffusion, with negligible numerical dissipation/diffusion, fully converged Direct Numerical Simulation (DNS)-like solutions are obtained when the ion Reynolds number based on the grid size is smaller than a threshold value which is about 2.3. For the magnetic reconnection problem, the results show that the magnetic flux saturation time and value converge when the ion and magnetic Reynolds numbers are large enough. Thus, the DNS-like results become relevant to practical problems with much larger Reynolds numbers.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

A BOUT++ extension for full annular tokamak edge MHD and turbulence simulations

For tokamak edge plasma simulation, a plasma simulation framework BOUT++ employs a dual coordinate system to simulate moderate-n and high-n plasma instability with reasonable computational cost, where n is the toroidal mode number. This coordinate system however limits the computational domain to the toroidal wedge (full torus divided into N parts in the toroidal direction) for computational efficiency and the use of flute-ordering approximation in the field solver calculating the flow potential from the vorticity which may not be valid for low-n modes. Improving numerical treatment of low-n modes is however indispensable to address simulations of low-n current-driven edge localized mode (ELM), ELM control by resonant magnetic perturbations (RMPs), edge turbulence with RMPs and so on. In this work, BOUT++ is extended to simulate the interplay between $n=0$, low-n and high-n plasma components in a full annular tokamak edge domain through hybrid modeling of the flow potential and the vorticity. Low-n modes of flow potential are calculated in an orthogonal flux surface coordinate and high-n modes in the dual coordinate system separately in Fourier space. Finally, the proposed scheme can capture an interplay between $n=1$ global modes and high-n turbulence during pedestal collapse in a full annular torus domain with a circular cross section.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Simulation of plasma transport in MPS-LD linear plasma device by using BOUT++

Here a linear plasma device (LPD) module based on the 2D transport module under the BOUT++ framework is developed in this paper to simulate plasma transport in the LPD. The LPD module includes three parts, i.e. magnetic field calculation, simulation mesh generation and plasma transport setup. The magnetic field is calculated with the circular current loop using the location and current information of each coil. The mesh generation code can produce a simulation mesh for LPD by employing the magnetic field. The plasma transport model is based on the reduced Braginskii equations, which consist of the continuity equation, momentum equation, and energy equation. The fluid neutral model is applied for neutral particle simulation. Deuterium (D) and helium (He) ions and atoms can be simulated by the model. The first attempt to simulate plasma transport in the new LPD, called multiple plasma simulation linear plasma device (MPS-LD), is presented using the developed model. The D plasma transport in the MPS-LD is simulated and benchmarked against the two-point model, showing the validation of the BOUT++ simulation. The effects of radial transport on the heat load to the target are studied, which illustrates the significant impact of the radial diffusivities $D_⟂$ and $\mathcal{X}_{⟂i,e}$ on the plasma. Moreover, the He impurity injection process during the discharge is studied with emphasis on plasma–impurity interactions. The simulation results show that He injection can reduce the plasma energy load to the target significantly, and the efficiency depends on the He source density and injection velocity. The present work provides an alternative and flexible simulation tool for plasma transport in LPDs.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Classical trajectory Monte Carlo simulation of plasma fueling using magnetic plasma expulsion

The possibility of fueling a magnetically confined plasma using particle sources located inside of the plasma is studied by computer simulation. Magnetic plasma expulsion [R. E. Phillips and C. A. Ordonez, Phys. Plasmas 25, 012508 (2018)] would serve to keep the magnetically confined plasma away from the particle sources without adversely affecting plasma confinement. The simulations show how charged particles can be injected into a plasma by using particle sources located directly between two current-carrying wires that create a magnetic expulsion field. Plasma fueling with the average energy of injected particles greater than the average energy of plasma particles may serve for heating the plasma. Also, plasma fueling with positive and negative particles injected at different rates may serve for changing the neutrality of the plasma. Conditions for plasma fueling are investigated using a classical trajectory Monte Carlo simulation. Two types of particle sources are considered, and the fraction of emitted particles that reach (and fuel) the magnetically confined plasma is evaluated for each.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Spectral solver for multi-scale plasma physics simulations with dynamically adaptive number of moments

A spectral method for kinetic plasma simulations based on the expansion of the velocity distribution function in a variable number of Hermite polynomials is presented. The method is based on a set of non-linear equations that is solved to determine the coefficients of the Hermite expansion satisfying the Vlasov and Poisson equations. In this paper, we first show that this technique combines the fluid and kinetic approaches into one framework. Second, we present an adaptive strategy to increase and decrease the number of Hermite functions dynamically during the simulation. The technique is applied to the Landau damping and two-stream instability test problems. Performance results show 21% and 47% saving of total simulation time in the Landau and two-stream instability test cases, respectively.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

PTRANSP Tests Of TGLF And Predictions For ITER

One of the physics goals for ITER is to achieve high fusion power PDT at a high gain QDT. This goal is important for studying the physics of reactor-relevant burning plasmas. Simulations of plasma performance in ITER can help achieve this goal by aiding in the design of systems such as diagnostics and in planning ITER plasma regimes. Simulations can indicate areas where further research in theory and experiments is needed. To have credible simulations integrated modeling is necessary since plasma profiles and applied heating, torque, and current drive are strongly coupled.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Efficacy of the radial pair potential approximation for molecular dynamics simulations of dense plasmas

Macroscopic simulations of dense plasmas rely on detailed microscopic information that can be computationally expensive and is difficult to verify experimentally. In this work, we delineate the accuracy boundary between microscale simulation methods by comparing Kohn–Sham density functional theory molecular dynamics (KS-MD) and radial pair potential molecular dynamics (RPP-MD) for a range of elements, temperature, and density. By extracting the optimal RPP from KS-MD data using force matching, we constrain its functional form and dismiss classes of potentials that assume a constant power law for small interparticle distances. Our results show excellent agreement between RPP-MD and KS-MD for multiple metrics of accuracy at temperatures of only a few electron volts. The use of RPPs offers orders of magnitude decrease in computational cost and indicates that three-body potentials are not required beyond temperatures of a few eV. Due to its efficiency, the validated RPP-MD provides an avenue for reducing errors due to finite-size effects that can be on the order of ∼20%.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

SciDAC-Center for Plasma Edge Simulation

The SciDAC ProtoFSP Center for Plasma Edge Simulation (CPES) [http://www.cims.nyu.edu/cpes/] was awarded to New York University, Courant Institute of Mathematical Sciences in FY 2006. C.S. Chang was the institutional and national project PI. It's mission was 1) to build kinetic simulation code applicable to tokamak edge region including magnetic divertor geometry, 2) to build a computer science framework which can integrate the kinetic code with MHD/fluid codes in multiscale, 3) to conduct scientific research using the developed tools. CPES has built two such edge kinetic codes XGC0 and XGC1, which are still the only working kinetic edge plasma codes capable of including the diverted magnetic field geometry. CPES has also built the code coupling framework EFFIS (End-to-end Framework for Fusion Integrated Simulation), which incubated and used the Adios (www.olcf.ornl.gov/center-projects/adios/) and eSiMon (http://www.olcf.ornl.gov/center-projects/esimmon/) technologies, together with the Kepler technology.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗